Not a hard quest, there are a lot of 1800's coins for under $60. Of course which ones you can get is going to depend on what denominations or quality you want. Lower grade Indian head cents can be had just a couple dollars. Mid-grade barbers, low to mid grade capped bust half, mid to higher end Braided hair cents, or even Mint State Morgans I'm not on top of prices but you could probably get a slabbed MS-63 1881-S
Morgan dollar for $60.